Towards unification
of genetic and hierarchy models of tumor heterogeneity

The cellular and molecular basis for intra-tumoral
heterogeneity is poorly understood. Tumor cells can be genetically
diverse due to mutations and clonal evolution resulting
in intra-tumoral functional heterogeneity. Often proposed
as mutually exclusive, cancer stem cell (CSC) models postulate
that tumors are cellular hierarchies sustained by CSC heterogeneity
due to epigenetic differences (i.e. long term tumor propagation
only derives from CSC). The clinical relevance of CSC has
been challenged by recent reports that some tumours may
actually not adhere to a CSC model when the xenograft system
is enhanced. Two lines of evidence support the CSC model
in AML and B-ALL. We have recently developed gene signatures
specific to either AML LSC or normal HSC and found they
share a set of genes that define a common stemness program.
Only these stem cell related gene signatures were found
to be highly significant independent predictors of patient
survival when large clinical databases were introgated.
Thus, determinants of stemness influence clinical outcome
of AML establishing that LSC are clinically relevant and
not artifacts of xenotransplantation. Second, we have carried
out a series of combined genetic and functional studies
of Ph+ B-ALL leukemic initiating cells (L-IC) that point
to commonalities between clonal evolution and CSC models
of cancer. L-IC from diagnostic patient samples were genetically
diverse and reconstruction of their genetic ancestry showed
that multiple L-IC subclones were related through a complex
evolutionary process that involved both linear or branching
leukemic progression. The discovery that specific genetic
events influence L-IC frequency and that genetically distinct
L-IC evolve through a complex evolutionary process indicates
that a close connection must exist between genetic and functional
heterogeneity. Finally, our study points to the need to
develop effective therapies to eradicate all genetic subclones
in order to prevent further evolution and recurrence.

Jasmine
Foo, University of MinnesotaModeling tumor heterogeneity and drug resistance

I
will discuss a stochastic model of tumorigenesis where
mutations confer random fitness changes sampled from a
distribution. We investigate the overall growth rate and
diversity of the population in the asymptotic limit, and
the dependence of these features on parameters of the
mutational fitness landscape. Using experimental data,
we apply this model to study characteristics of a drug-resistant
subpopulation in chronic myeloid leukemia. We also consider
the impact of treatment strategies and compliance on the
development of resistance in EGFR mutant non-small cell
lung cancer using tyrosine kinase inhibitors.

A
number of successful systemic therapies are available
for treatment of disseminated cancers. However, tumor
response is often transient and therapy frequently fails
due to emergence of resistant populations. The latter
reflects the temporal and spatial heterogeneity of the
tumor microenvironment as well as the evolutionary capacity
of cancer phenotypes to adapt to therapeutic perturbations.
Although cancers are highly dynamic systems, cancer therapy
is typically administered according to a fixed, linear
protocol. An alternative approach, termed adaptive therapy,
evolves in response to the temporal and spatial variability
of tumor microenvironment and cellular phenotype as well
as therapy- induced perturbations. Initial mathematical
models find that when resistant phenotypes arise in the
untreated tumor, they are typically present in small numbers
because they are less fit than the sensitive population.
This reflects the "cost" of phenotypic resistance
such as additional substrate and energy utilized to upregulate
xenobiotic metabolism and, therefore, not available for
proliferation, or the growth inhibitory nature of environments
(i.e. ischemia or hypoxia) that confer resistance on phenotypically
sensitive cells. Thus, in the Darwinian environment of
a cancer, the fitter chemo-sensitive cells will ordinarily
proliferate at the expense of the less fit chemo-resitant
cells. The models demonstrate that, if resistant populations
are present prior to administration of therapy, treatments
designed to kill maximum numbers of cancer cells removes
this inhibitory effect and actually promotes more rapid
growth of the resistant populations. We present an alternative
approach in which treatment is continuously modulated
to achieve a fixed tumor population. The goal of adaptive
therapy is to enforce a stable tumor burden by permitting
a significant population of chemosensitive cells to survive
so that they, in turn, suppress proliferation of the less-fit
but chemo-resistant subpopulations. Computer simulations
demonstrate this strategy can result in prolonged survival
that is substantially in greater than that of high dose
density or metronomic therapies. The feasibility of adaptive
therapy is supported by in-vivo experiments.

Metastatic spread of cancer is very often the ultimate
cause of death in patients. Yet the efficiency with which
cancer cells form metastases appears to be very low. Multiple
possible causes for this inefficiency have been proposed,
including surmounting multiple steps in the metastatic
process as well as low percentages of stem cells in tumours
but the exact mechanisms remain unclear and may be both
heterogeneous and different for different cancers. Recent
studies have also suggest the induction of metastatic
niches in certain organs in the body that may specifically
support the development of metastases. The microenvironment
of the primary tumour, particularly hypoxia, can also
influence metastasis formation and may predispose to the
formation of such niches. Understanding and predicting
the presence of micrometastases prior to their detectability
by imaging could identify patients who need more aggressive
initial treatment.

Harsh
Vardhan Jain, Mathematical Biosciences Institute, The
Ohio State University

In
this talk, I will present a new approach to anti-cancer
therapy modeling that reconciles existing observations
for the combined action of carboplatin (a Pt-based chemotherapeutic
agent) and ABT-737 (a small molecule inhibitor of Bcl-2/xL)
against ovarian cancers. To accurately simulate the action
of these drugs, an age-structure together with a delay
is imposed on proliferating cancer cells, and intracellular
signaling pathways relevant to drug action explicitly
modeled. The resultant delayed partial differential equation
(PDE) model thus accounts for cell cycle arrest and cell
death induced by chemotherapy. The model is calibrated
versus in vitro experimental results, and is then used
to predict optimal doses and administration time scheduling
for the treatment of a tumor growing in vivo.

Mohammad
Kohandel, University of Waterloo

Quantitative
approaches to cancer stem cell hypothesis

The
last decade has witnessed significant advances in the application
of physical, mathematical and computational models to biological
systems, especially to cancer biology. In this presentation,
we examine mathematical models describing tumour growth
based on the cancer stem cell hypothesis, and present the
application of these models to various cancer treatments,
as well as to the epithelial-mesenchymal transition. In
addition, we discuss how quantitative approaches can be
used to investigate the tumour heterogeneities exposed to
various microenvironmental conditions of the cancerous tissue.
Finally, the role of the mesenchymal transition and neural
stem cells, and their mutual interaction, in molecular subtypes
of glioblastoma multiforme, are presented based on genetic
data.

Natalia
Komarova, University of California, Irvin
Cellular cooperation as a pathway to cancer (slides)

Cancer
comes about by a sequence of mutations that change the
cells' fitness and create advantageous phenotypes. These
phenotypes displace other cells and spread, thus winning
the evolutionary competition. It is possible that in order
to create those advantageous mutants, several different
mutations have to be accumulated in a cell, such that
each individual mutation is disadvantageous, and together
they comprise a fitness advantage. In the literature,
this is often called "crossing a fitness valley".
In this talk I will present a novel mechanism by which
such fitness valleys can be crossed. It envolves the notion
of cooperation among the cells. I will show how cooperation
can speed up the evolutionary process.

Despite
considerable advances in our understanding of tumor biology
at the primary site, metastasis remains a major cause for
the majority of carcinoma-related mortalities. Metastasis
is a complex multi-step process, wherein tumor cells detach
from the initial site, invade the surrounding stroma, intravasate
and survive in the circulation, extravasate at distant organs
to form micrometastases. Eventually, a few of these micrometastatic
colonies expand to become macrometastatic nodules. Studies
have shown that the activation of a latent embryonic program-epithelial-mesenchymal
transition (EMT) plays a critical role in cancer metastasis.
Independently, Cancer Stem Cells (CSCs) are also shown to
play a central role in tumor initiation and tumor progression.
Recently, we and others have found that the CSCs could be
generated from differentiated cells through the activation
of EMT program. These findings uncovered a unique window
of opportunity and suggests that the CSCs could be targetted
using the EMT pathways. My presentation will summarize our
current effort in understanding of the EMT pathways and
their relevance to breast cancer progression.

Cancer development is an evolutionary process within an
organism: cells acquire mutations, compete for resources,
and are subject to natural selection. During this transformation,
malignant tissues acquire tens of thousands of somatic mutations,
yet only a handful, called driver alterations, are believed
to be responsible for the cancer phenotype. The vast majority
of remaining alterations are called passenger alterations
and believed to be evolutionarily neutral in phenotype.
Our hypothesis is that many passengers are deleterious to
cancer cells, yet still accumulate.

We developed a novel stochastic population genetics model
of cancer progression where cells can acquire both advantageous
driver and deleterious passenger mutations. We found that
mildly deleterious passengers accumulate in populations
by both mutational ratcheting and by hitchhiking with drivers,
and that their accumulation can slow or revert neoplastic
progression. Using comparative genomics, we analyzed known
driver and passenger mutations and found that many passengers
possess deleterious phenotype--corroborating our model.

Using combined numerical and analytical analysis, we discovered
two phases of cancer dynamics: one where driver mutations
dominate and populations grow exponentially, and another
where deleterious passengers overwhelm populations, resulting
in prolonged dormancy or extinction. This phase transition
results from a critical population size,
akin to a activation barrier, that populations must first
overcome to progress to cancer. Interestingly, there exists
an optimal mutation rate for cancer. Low mutation rates
lead to slow driver accumulation, while very high rates
prevent cancer development because drivers typically arise
in cells with an excessively damaging load of passenger
mutations that prevents clonal expansion. Our results explain
observed clinical patterns of mutations and patient outcomes.

Finally, we compare therapeutic strategies that could exploit
the effects of these deleterious passenger alterations.

Cervical cancer, like other human tumors, is characterized
by an abnormal vascular network that develops because
of unregulated angiogenesis. This, in turn, is an important
determinant of microenvironmental abnormalities like hypoxia,
acidosis and high interstitial fluid pressure (IFP) that
influence treatment response and patient survival. There
is an important clinical need to develop new minimally
invasive tools for characterizing the tumor microenvironment
at diagnosis, and monitoring changes during treatment
with radiotherapy, chemotherapy or new biologically targeted
drugs. MR and PET-based imaging approaches offer exciting
possibilities that have yet to be fully exploited. Dynamic
contrast enhanced (DCE) MR allows the functional characteristics
of the tumor vasculature to be interrogated serially over
time. Studies in cervical cancer have shown substantial
differences in DCE MR parameters between tumor and normal
muscle in keeping with higher blood flow and vascular
permeability, and substantial variation in these parameters
from one tumor to the next and within individual tumors.
Pre-treatment DCE MR has been shown to correlate with
response to radiotherapy or drugs that specifically target
the tumor vasculature. MR techniques have also been used
to assess tumor interstitial fluid dynamics and IFP, using
either conventional low molecular weight contrast agents
or new liposomal agents. PET imaging of tumor perfusion
and hypoxia using radiolabeled nitroimidazole tracers
is being investigated in clinical studies. Despite important
advances, none of these approaches has been adopted in
routine clinical practice because of a lack of consensus
on optimal imaging techniques, analysis methods and reporting
metrics. Further refinement and standardization is required
founded on interdisciplinary collaboration among clinicians,
medical imagers, biologists, physicists and mathematicians
to make these techniques robust and clinically applicable.

Colin
Phipps, University of Waterloo

Mathematical
model for angiogenic behaviour in solid tumours:

A mathematical model is presented for the concentrations
of proangiogenic and antiangiogenic growth factors, and
interstitial fluid pressure, in solids tumours embedded
in host tissue. In addition to production, diffusion, and
degradation of these angiogenic growth factors (AGFs), we
include interstitial convection to study the locally destabilizing
effects of interstitial fluid pressure (IFP) on the angiogenic
activity endowed by these factors. The molecular sizes of
representative AGFs and the outward flow of interstitial
fluid in tumors suggest that convection is a significant
mode of transport for these molecules. The resulting balance
or imbalance of proangiogenic and antiangiogenic serves
as a possible mechanism for determining whether blood vessels
are stable, developing or regressing. The results of our
modeling approach suggest that changes in the physiological
parameters that determine interstitial fluid pressure have
as profound an impact on tumor angiogenesis as those parameters
controlling production, diffusion, and degradation of AGFs.
This model has predictive potential for determining the
angiogenic behavior of solid tumors and the effects of cytotoxic
and antiangiogenic therapies on tumor angiogenesis.

Typical
cell proliferation assays estimate cell counts at fixed
time-points, not dynamically. In the presence of perturbations
affecting proliferation, they provide little information
on underlying individual cellular behaviors (e.g., apoptosis,
decreased cell division rate, etc.). We present Fractional
Proliferation, an integrated method, based on extended time-resolved
automated microscopy that quantifies cell proliferation
dynamics in response to perturbations by integrating population-
and single-cell level. Direct cell count data, collected
every 6 minutes, are initially fit with a novel Quiescence-Growth
mathematical model, based on three parameters: division,
death and quiescence rates. This model is then substantiated
by extracting these rates from experimental observations
of hundreds of single cells, fitted with an Exponentially
Modified Gaussian model. In the final output graphs, Fractional
Proliferation describes the underlying behavioral dynamics
that result in proliferative changed by perturbations. Using
this method, we discovered that the response of cell lines
to erlotinib, an epidermal growth factor receptor tyrosine
kinase inhibitor, is a nonlinear process dominated by an
increased rate of cell entry into quiescence. Even in highly
sensitive "oncogeneaddicted" cells, quiescence
prevailed, with only a modest increase in death rate. Similar
results were obtained with oncogene-addicted melanoma and
breast cancer cell lines treated with the respective targeted
oncogene inhibitors. In contrast to our results, drug targeting
of addicting oncogenes has thus far been thought to result
in massive cell death. Instead, our findings indicate that
it may cause response behaviors other than death, underscoring
the realistic in vitro representation of cell proliferative
response to perturbagens provided by Fractional Proliferation,
and providing means to optimize and improve discovery and
deployment of targeted therapy.

Medulloblastoma
stem cells: where development and cancer cross pathways
(slides)

Brain tumours represent the leading cause of childhood
cancer mortality, with medulloblastoma (MB) representing
the most frequent malignant tumor. Due to morphological
similarities between MB cells and proliferating external
granule cells of the postnatal cerebellum, recent studies
have merged cancer genomics and developmental biology
approaches to demonstrate the presence of different MB
molecular subtypes. The identification of cancer stem
cell populations, termed brain tumour initiating cells
(BTICs), in MB has provided novel cellular targets for
the study of aberrantly activated signaling pathways,
namely Sonic hedgehog and Wingless, along with the identification
of novel BTIC self-renewal pathways. Here, we discuss
recent evidence for the presence of a MB stem cell, which
may drive tumorigenesis in the most aggressive subtypes
of this malignant childhood tumour. We focus on evidence
from cerebellar development, the recent identification
of BTICs, the presence of activated developmental signaling
pathways in MB, the role of epigenetic stem cell regulatory
mechanisms, and how these developmental and epigenetic
pathways may be targeted with novel therapeutic options

Nanoformulations~of chemotherapeutic drugs are increasingly
being studied for their potential to improve efficacy
and safety. However, limited studies have been done on
sequential dosing of nanochemotherapeutics and signal
transduction inhibitors.

In this study, we determined the optimal combination regimen
of PI-3 kinase inhibitor PI828 and cisplatin nanoparticles
in~murine breast cancer model to achieve maximal cell
killing. Western blot analysis showed a time dependent
upregulation of phospho- AKT expression after administration
of cisplatin nanoparticles. We also observed a time dependent
decrease in expression of XIAP which corroborated with
an increased expression of Cleaved Caspase-3. PiAkt overexpression
induced by cisplatin liposome was was efficiently suppressed
by PI828 in the post-treatment schedule resulting in significantly
increased apoptosis as measured by Caspase-3 expression.
The upregulation of piAKT dependent signalling was mediated
by both an EGFR dependent downstream activation of PI3
kinase pathway and an increased nuclear transcription
of Akt gene.

A simple mathematical model using the quantitative expression
of the above
mentioned cellular proteins( piAKT, Cleaved Casapse-3
and XIAP) was designed to predict the optimal combination
regimen of the two drugs . The mathematical model predicted
that a combination regimen using PI828 for after 24-36
hurs Cisplatin nanoparticle therapy would achieve maximal
cell killing.

In vitro cell proliferation assay validated the modeling
results with PI828
post-treatment showing significantly increased cell death
as compared to controls and pretreatment.

In a 4T1 syngenic murine cancer model, post-treatment
with PI828 following
cisplatin nanoparticles treatment significantly suppressed
tumour growth as
compared to the pre-treatment or nanoparticles alone.
These results indicate that sequence of administration
of signal transduction inhibitors like PI828 can
impact the outcome of treatment with cisplatin nanotherapeutics.

Large-scale sequencing and gene profiling of cancer genomes
have generated huge amount of data. It is increasingly
realized that these information could be useful in guiding
personalized care and treatment to cancer patients. However,
it is very challenging in how to making sense of and making
use of these data toward personalized medicine.

I will talk about using network approach to analyze tumor
signaling networks to get insights and developing new
algorithms to get cell-specific drug targets, and molecular
markers for prognosis and drug response.

Kathleen Wilkie, Center of
Cancer Systems Biology, Tufts University School of MedicineA Mathematical Model of Immune Modulation of Tumor
Growth

Cancer
cells can elicit an immune response in the host, which
is generally tumor-suppressive, but for weak responses
may actually be tumor-promoting. We propose that this
complex dynamic may be understood as a process of immune
stimulation by the tumor, followed by cytotoxic targeting
by the immune cells, which acts to alter tumor size and
growth characteristics and subsequent immune stimulation.
Just how these influences interact has complex implications
for tumor development and cancer dormancy. To show this,
we have developed a two-compartment model consisting of
a population of cancer cells and a population of immune
cells. The model incorporates the combined effects of
the various immune cell types, exploiting general principles
of self-limited logistic growth and the physical process
of tumor-promoting inflammation. A Markov chain Monte
Carlo method is used to determine parameter sets that
predict tumor growth equally well, but at the same time
also predict fundamentally different underlying dynamics.
The results underscore the ultimately polar nature of
final tumor fate (escape or elimination), while at the
same time showing how persistent regions of near-dormancy
may precede either of these two outcomes. Another important
finding is that near-{} and long-term responses of a tumor
to immune interaction may be opposed; that is to say,
a response dynamic that appears to be more promoting of
tumor growth than another in the near term may be superior
at curtailing tumor growth in the long-term, even to the
point of establishing dormancy while the other allows
for tumor escape. The striking variability observed even
in this simple model demonstrates the significance of
intrinsic and unmeasurable factors determining the complex
biological processes involved in tumor growth in an immune
competent host. Consequences and biological interpretations
of this work will be discussed in terms of treatment approaches
that exploit immune response to improve tumor suppression,
including the potential attainment of an immune-induced
dormant state.Kathleen Wilkie and Philip Hahnfeldt

Spatial and temporal variations in oxygen are observed in
the majority of solid tumours and function as a major contributor
to phenotypic diversity and a significant barrier to current
curative treatment approaches. Tumor hypoxia elicits profound
changes in cell behaviour through multiple mechanisms that
influence cellular metabolism, genetic stability, angiogenesis,
and self-renwal. In this session, I will review recent discoveries
of oxygen-sensitive signalling pathways that help to explain
these phenotypes including activation of the unfolded protein
response (UPR) and regulation of autophagy. These new findings
help to explain the adverse effect of hypoxia on tumor behaviour
but also reveal potential therapeutic targets for improving
treatment efficacy.